The Apostle Paul writing to the church in Rome puts it frankly in Corinthians 12:27 "Now you are the body of Christ, and each one of you is a part of it." Or in other words, each of us that are "born again Christians" are a part of that "body of Christ". The Apostle Paul further emphasizes in 1 Corinthians 12:12 what that "body" is: "The body is a unit, though it is made up of many parts; and though all its parts are many, they form one body. So it is with Christ." That makes each of us a unique and important part of that "one body".
The Apostle Paul writing to the church in Ephesus helps to clarify the purpose or objective of the "body of Christ" in Ephesians 4:12-13 "to prepare God's people for works of service, so that the body of Christ may be built up 13 until we all reach unity in the faith and in the knowledge of the Son of God and become mature, attaining to the whole measure of the fullness of Christ." In other words, we are all part of the "body of Christ" and should be doing some sort of "works of service" so that all Born again Christians ("body of Christ") may learn, grow, and come together in the same faith and knowledge of Jesus.
It all boils down to developing Christian Community. Whether it be churches, assemblies, bible studies, prayer groups, etc...
The Apostle Paul in 1 Corinthians 12:12-31 gives us numerous facets regarding the structure of the "body of Christ":
In verse 12 the body "... is made up of many parts ..." meaning that each of us are a unique part.
Also in verse 12 the "... body is a unit ..." and is "... one body... ". The whole body is a single entity.
When anyone accepts Jesus as their personal savior [refer to "Salvation"] they receive the Holy Spirit as described in verse 13 "For we were all baptized by one Spirit into one body..." The emphasis should be made here that the "one body" is the "body of Christ".
Verses 14-17 uses easy to understand human body parts to describe the importance and uniqueness of each part.
Then verse 18 caps it off and puts value to each of the parts: "But in fact God has arranged the parts in the body, every one of them, just as he wanted them to be." In other words, we are each unique, put in our unique position, with God given talents and abilities.
In verses 21-24 the emphasis is on the value of the lesser "parts": "... But God has combined the members of the body and has given greater honor to the parts that lacked it, ..." Which means that non of us can claim that our talents and/or abilities are of no value.
The next couple of verses are against any kind of division amongst the parts. In verse 25 "... there should be no division in the body ...". This would apply, not only to talents and abilities, but also belief and conviction.
The result of division is described in verse 26: "If one part suffers, every part suffers with it; if one part is honored, every part rejoices with it."
Verse 27 declares who the "body of Christ" is: "Now you are the body of Christ, and each one of you is a part of it."
Verses 28-31 describe the make-up of God's church. With a special emphasis at the end regarding the primary goal in verse 31 "But eagerly desire the greater gifts." Which would be God's blessings and eventually eternity with Him.
To the secular world, the "body of Christ", if it means anything at all, probably refers to Jesus' body. The more educated may know that it refers to Christians, but usually with no emphasis on its origin or sense of unity.
Essentially, all Born again Christians are a part of the "body of Christ". Each of us are a part of that "one body" and have been given unique talents and/or abilities. No matter how small those talents and/or abilities may seem, God's Word impresses upon us that each of us need to exercise them to their fullest for the up lifting and growth of the entire body. Essentially, it all boils down to our own personal responsibility to God to do our best for the "body of Christ".